You got the perfect metaphore. To avoid rats, you don't kill them or set traps, you do trash collection, so you make a friendly environment for clean animals and not for those which bring plague. You can do the same: have integration courses, make VISAs readily available for everyone no question asked, put language courses in place and make everyone in condition to have a job and contribute to society. The United States is a country made of migrants. Almost no one is a "native american" there. Wasn't that the most powerful country in the world, up to 10 years ago? So, "native Britons" is a sentence that makes no sense, and it's racist.